Question

Suppose you exert a force of 314 N tangential to a grindstone (a solid disk) with a radius of 0.281 m and a mass of 84.2 kg What is the resulting angular acceleration of the grindstone assuming negligible opposing friction

Answer 1

The angular acceleration is 26.6 rad/s^2.

Step-by-step explanation:

Force, F = 314 N

radius, r = 0.281 m

mass, m = 84.2 kg

The grindstone is a disc.

The torque is given by

torque = force x radius

Torque = 314 x 0.281 = 88.234 Nm

The torque is given by

Torque = Moment of inertia x angular acceleration

`88.234 = 0.5 mr^2 \alpha \\\\88.234 = 0.5* 84.2* 0.281* 0.281* \alpha \\\\\alpha = 26.6 rad/s^2`